Heat olive oil in a large skillet over medium heat. Cook and stir mushrooms and onion in hot oil until softened, about 5 minutes. Remove from heat and set aside.
Melt 2 tablespoons of butter in a stockpot over medium heat. Cook quinoa in melted butter until lightly brown. Pour enough stock to just cover the quinoa. Allow the liquid to reduce to half. Continue this process until quinoa is soft and all stock is absorbed, about 30 minutes. Season with salt throughout process.
Stir mushrooms, onion, and tuna through the quinoa; season with black pepper. Stir 1/4 cup butter, the egg, and flour into the quinoa mixture; transfer to a casserole dish and top with bread crumbs to cover.
Bake until the top is golden brown and the center is hot, about 30 minutes.